The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

The correct answer is 8%.

To find the maximum error in the estimation of the kinetic energy, we begin with the formula for kinetic energy ($K$):
$K=\frac{1}{2}m{v}^2$
where:
$m$ represents the mass of the body, and
$v$ represents the speed of the body.

The relative error in a product or quotient of quantities is the sum of the relative errors of the individual quantities multiplied by their respective powers. For kinetic energy, the constant factor $\frac{1}{2}$ does not contribute to the error. Therefore, the maximum relative error in kinetic energy ($\frac{\Delta K}{K}$) is given by:
$\frac{\Delta K}{K}=\frac{\Delta m}{m}+2\left(\frac{\Delta v}{v}\right)$

To express this as a percentage error, we multiply each term by 100:
$\frac{\Delta K}{K}\times 100=\left(\frac{\Delta m}{m}\times 100\right)+2\left(\frac{\Delta v}{v}\times 100\right)$

We are given the following percentage errors:
Percentage error in mass ($\frac{\Delta m}{m}\times 100$) = 2%
Percentage error in speed ($\frac{\Delta v}{v}\times 100$) = 3%

Substituting these values into our error equation:
$\text{Maximum percentage error in K}=2\%+2(3\%)$
$\text{Maximum percentage error in K}=2\%+6\%=8\%$

Thus, the maximum error in the estimation of the kinetic energy is 8%.